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If w=z/[z-(1/3)i] and |w|=1, then find ...

If `w=z/[z-(1/3)i]` and `|w|=1,` then find the locus of `z`

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To find the locus of \( z \) given the equation \( w = \frac{z}{z - \frac{1}{3}i} \) and the condition \( |w| = 1 \), we can follow these steps: ### Step 1: Write the equation with modulus Given that \( |w| = 1 \), we have: \[ |w| = \left| \frac{z}{z - \frac{1}{3}i} \right| = 1 \] ...
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CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
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  2. The total number of integral values of a so that x^2-(a+1)x+a-1=0 has ...

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  3. If w=z/[z-(1/3)i] and |w|=1, then find the locus of z

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  4. Let C1and C2 be two circles with C2 lying inside C1 A circle C lying i...

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  5. The number of positive integral solutions of x^4-y^4=3789108 is a.0 ...

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  7. z1, z2, z3,z4 are distinct complex numbers representing the vertices o...

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  8. If alpha,beta are the roots of x^2+p x+q=0a n dx^(2n)+p^n x^n+q^n=0a n...

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  9. If (log)(sqrt(3))((|z|^2-|z|+1)/(2+|z|))>2, then locate the region in ...

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  10. If z=((1+isqrt3)^2)/(4i(1-isqrt3)) is a complex number then a. arg(...

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  11. If alpha,beta,gamma are such that alpha+beta+gamma=2,""alpha^2+beta^2+...

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  12. If z=3/(2+costheta+"isin"theta) then locus of z is straight line a c...

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  13. If z=x +i y such that |z+1|=|z-1| and arg((z-1)/(z+1))=pi/4 , then fin...

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  14. If x y=2(x+y),xlt=y and x ,y in N , then the number of solutions of t...

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  15. If I m((z-1)/(e^(thetai))+(e^(thetai))/(z-1))=0 , then find the locus ...

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  16. If pa n dq are distinct prime numbers, then the number of distinct im...

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  17. The number of real solutions of the equation (9//10)^x=-3+x-x^2 is a. ...

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  18. What is locus of z if |z-1-sin^(-1)(1/sqrt3)|+|z+cos^(-1)(1/sqrt3)-p...

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  19. If |z-2-i|=|z|sin(pi/4-a r g z)| , where i=sqrt(-1) ,then locus of z,...

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  20. The number of integral values of a for which the quadratic equation (x...

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